Let $f$ be a function of $t$ for $t0$ with a well$-$defined Laplace Transform hat$(f)(s).$ The

transform has the property

$g(t)=tf(t)=>$hat$(g)(s)=-\frac{d}{ds}$hat$(f)(s).$

A function $q$ is defined for $t0$ as follows:

$\frac{d^{2}x}{(d)t^2}+5\frac{dx}{(d)t}+6x=f(t)x(t)f(t)\frac{1}{x^2+5x+6}=\frac{1}{x+2}-\frac{1}{x+3}.$